The rise of the papacy is important for a number of reasons. We will look at two of them here.
First, the rise of the papacy helped to create a powerful Catholic Church. By unifying the Church (for example, by helping to set one orthodox set of belief and scripture) the rise of the papacy helped to create a situation in which there was one church that was unopposed in its dominance of spiritual matters.
Second, the rise of the papacy helped to create the idea of Europe. This, too, was done by the fact that it created a single Christian church, one that was closely connected to Rome. This allowed one Christian faith to spread across Western Europe, giving the whole area a common basis for its culture and helping to create a European culture.